Step 1Pick over the beans and soak in water to cover by at least 2 inches for 12 hours.
Step 2The following day, rinse and drain the beans and set aside. Meanwhile, in a heavy 4- to 5-quart flameproof pot, preferably earthenware, such as a Yankee bean pot or a Chinese sand pot, gently cook the carrots and onions in 2 tablespoons of the duck fat, stirring until tender, 5 to 10 minutes. Scoop out and reserve about one-fourth cup of the onions and carrots. Add the drained beans and 2 quarts fresh water to the pot. Bring to a boil, reduce the heat to moderately low, add a pinch of salt and pepper, and simmer for 2 hours, or until the beans are tender and the liquid is reduced.
Step 3In a medium skillet, heat the remaining duck fat. Add the diced bread, slivered ventreche and the reserved carrots and onions. Fry, stirring until crisp. Remove to a side dish, add the chives, and set aside.
Step 4Let the beans cool slightly, scoop out about one-third cup for garnish and set aside. Press batches of the remaining beans and liquid through the fine blade of a food mill or puree in a food processor or blender. Add the bean puree to the soup pot. Stir in the cream [Note: the Test Kitchen recommends adding 1 1/2 to 2 cups water to the pureed beans to create a thick soup consistency], bring to a boil and simmer for 5 minutes. Correct the seasoning with salt, pepper and red pepper to taste.
Step 5To serve, divide the reserved beans among the soup bowls, ladle the hot soup over the beans, and garnish each portion with a spoonful of the fried onion and ventreche mixture. Serve at once.